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IIB Algebra 1.27

 
 
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IIB Algebra 1.27
ZhangDaniel - 2024年05月11日 Saturday 14:04
 

The question is a3b−ab3+a2+b2+1�3�−��3+�2+�2+1. I tried factoring out an ab from the first two terms, giving me ab(a^2-b^2), or ab(a-b)(a+b), but how would I combine this with a^2+b^2+1?

 
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Re: IIB Algebra 1.27
LinXilong - 2024年05月12日 Sunday 21:58
 

Since we have ab, (a - b) and (a + b), we can try subtracting an ab after a^2 and adding an ab after b^2. This will make the expression be like\( ab(a - b)(a + b) + a(a - b) + b(a + b) + 1 \). If we regard a(a - b) as X and b(a + b) as Y, it will be like XY + X + Y +1, which is equal to (X + 1)(Y + 1).

 
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ZhangDaniel的头像
Re: IIB Algebra 1.27
ZhangDaniel - 2024年05月13日 Monday 10:14
 
Oh, I see. Thank you so much! For the final answer, would I have to expand out the two terms, or could I keep it as [a(a-b)+1][b(a+b)+1]?
 
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